Solve Ay-B=C_{y}+7C

$$A y - B = C _ { y } + 7 C$$

Solve for A (complex solution)

$$\left\{\begin{matrix}A=\frac{B+C_{y}+7C}{y}\text{, }&y\neq 0\\A\in \mathrm{C}\text{, }&B=-C_{y}-7C\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add B to both sides.

$$Ay=C_{y}+7C+B$$

The equation is in standard form.

$$yA=B+7C+C_{y}$$

Divide both sides by y.

$$\frac{yA}{y}=\frac{B+7C+C_{y}}{y}$$

Dividing by y undoes the multiplication by y.

$$A=\frac{B+7C+C_{y}}{y}$$

Divide B+7C+C_{y} by y.

$$A=\frac{B+C_{y}+7C}{y}$$

Solve for A

$$\left\{\begin{matrix}A=\frac{B+C_{y}+7C}{y}\text{, }&y\neq 0\\A\in \mathrm{R}\text{, }&B=-C_{y}-7C\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add B to both sides.

$$Ay=C_{y}+7C+B$$

The equation is in standard form.

$$yA=B+7C+C_{y}$$

Divide both sides by y.

$$\frac{yA}{y}=\frac{B+7C+C_{y}}{y}$$

Dividing by y undoes the multiplication by y.

$$A=\frac{B+7C+C_{y}}{y}$$

Divide B+7C+C_{y} by y.

$$A=\frac{B+C_{y}+7C}{y}$$

Solve for B

$$B=Ay-C_{y}-7C$$

Steps for Solving Linear Equation

Subtract Ay from both sides.

$$-B=C_{y}+7C-Ay$$

The equation is in standard form.

$$-B=7C+C_{y}-Ay$$

Divide both sides by -1.

$$\frac{-B}{-1}=\frac{7C+C_{y}-Ay}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$B=\frac{7C+C_{y}-Ay}{-1}$$

Divide C_{y}+7C-Ay by -1.

$$B=Ay-C_{y}-7C$$